5 October 2015
Issue no. 171
Tales of rice and rewards
The story goes that a king in India was so impressed by the new
game of chess that he offered the wise sage who invented it any gift
of his choosing. The sage modestly asked to be paid in grains of rice:
the king was to put a single grain of rice on the first chess square and
double it on every subsequent square.
The king readily agreed and ordered a bag of rice to be brought to
the chessboard. He then started placing rice grains according to the
arrangement: one grain on the first square, two on the second, four
on the third, eight on the fourth, and so on. Following the exponential
growth of the rice payment, the king soon realised that he would be
unable to fulfil his promise. On the 20th square he would have had
to put 220 or just over 1 000 000 grains of rice. With 264 grains and
48 grains per gram of rice, the king would have had to put more
than 380 billion tons on the last square. That is 500 times this year’s
global rice production forecast.
How is a fable about exponential mathematical series relevant
to investing?
Graph 1 illustrates two investment strategies. Investor 1 began
investing R1 000 a month in the year 2000 into a balanced fund. He
contributed monthly until the end of 2004, a total of 60 contributions
or R60 000, at which stage he stopped contributing, but left his
money invested until the end of 2014.
Investor 2 began contributing R1 000 per month from the beginning
of 2005 into the same balanced fund, and continued to contribute
until the end of 2014. A total of 120 contributions, double the capital
contribution of investor 1.
Graph 1 shows that although investor 1 contributed 50% less than
investor 2, his investment is worth a significant 40% more. On top
of this, less than a quarter of the final amount has come from his
pocket. The rest is from investment returns and compound interest.
Graph 1
The power of compound interest
Value of investment
R360 000
R300 000
R240 000
R180 000
R250 269.43
R100 087.22
R120 000
R60 000
R0
Contributions
Growth of
investment
How does this work?
Similar to the rice story, as your investment begins to earn returns,
the base from which it will earn future returns grows exponentially.
Although investor 1 contributed less money, he had already
accumulated a fair amount by the time investor 2 started to invest.
This is illustrated in Graph 2, which uses the same data as Graph 1,
but shows the market growth of the investments.
Graph 2
R350 000
Value of investment
We often talk about the value of time in investing, but it is difficult
to really get to grips with the rewards that can be reaped through
compound growth: earning interest today on interest earned
yesterday and so forth. The power of exponential growth is neatly
demonstrated by the rice and chessboard story, the earliest record
of which is in an epic poem written in Persia about 1 000 years ago.
R300 000
Time in the market
Investor 1 stops
contributions and investor 2
starts contributions
R250 000
R200 000
R150 000
Investor 1
Investor 2
R100 000
R50 000
R0
Source: Morningstar, Allan Gray
Is now the right time to invest?
The rand is currently weaker than it has been for some time, and
there are crises unfolding in different corners of the globe. At the
same time, local equities are, on the whole, looking expensive.
Investors are understandably confused about where to put their
money, and are asking ‘when is the right time to invest?’
In the absence of a crystal ball, it is impossible to accurately predict
what will happen next on the markets; we simply do not know. We do
know that if we look back over time, clients who have started early
and left their investments to grow, have performed better than those
who kept putting off investing, hoping that market conditions would
improve.
If you are concerned about equity valuations, or feel you need to
diversify asset classes but don’t know how to do it, you may wish to
consider a solution unit trust, such as a balanced fund. In a balanced
fund you hand over the asset allocation and timing decisions to an
experienced fund manager, who makes the decisions for you.
For most of us, procrastination is the enemy. Market ups and downs
tend to smooth out over time, rewarding long-term investors. Time in
the market is critical if you truly want to benefit from the wonders of
compounding.
If the Persian poet who penned that story had invested the price of a
scraggly goat (say US$10 in today’s money) at a real return of 3%,
leaving the proceeds to the Persian (now Iranian) people, and found
a way to stay invested through the 1 000 years since then, his legacy
would be equal to about 250 times Iran’s current GDP.
R120 000
R60 000
Investor 1
Investor 2
Data is based on the average return of unit trusts in the South African – Multi Asset –
High Equity category. Nominal returns are shown, i.e., they do not take inflation into
account. Contributions are held constant, i.e. they do not increase with inflation.
Source: Morningstar, Allan Gray
Commentary by Jeanette Marais, director of distribution and client service
Allan Gray Unit Trust Management (RF) Proprietary Limited (the ‘Management Company’) is registered as a management company under the Collective Investment Schemes Control Act 45 of 2002.
Allan Gray Proprietary Limited (the ‘Investment Manager’), an authorised financial services provider, is the appointed investment manager of the Management Company and is a member of the
Association for Savings & Investment South Africa (ASISA). Collective Investment Schemes in Securities (unit trusts or funds) are generally medium- to long-term investments. Except for the Allan
Gray Money Market Fund, where the Investment Manager aims to maintain a constant unit price, the value of units may go down as well as up. Past performance is not necessarily a guide to future
performance. The Management Company does not provide any guarantee regarding the capital or the performance of its unit trusts. Funds may be closed to new investments at any time in order for
them to be managed according to their mandates. Unit trusts are traded at ruling prices and can engage in borrowing and scrip lending. Performance figures are for lump sum investments with income
distributions reinvested. Actual investor performance may differ as a result of the investment date, the date of reinvestment and dividend withholding tax.